Obi-Wan: For over a thousand generations, the Jedi knights were the guardians of peace and justice in the old Republic... before the dark times... before the empire.

For me, it's actual membership in the Jedi order. There are some grey areas around the edges - an apprentice who is trained by a master and never gets to meet the council or formally become one, a person like Count Dooku who leaves the order but you still kind of think of as a Jedi. But basically it's about affiliation to the beliefs or organization. Someone who is Force-sensitive is not inherently a Jedi. Someone trained in lightsabre use is not inherently a Jedi.

And it most definitely is NOT someone who happens to have a high midichlorian count. *spit*